Open Access

ARTICLE

The Boundary Element Method for Ordinary State-Based Peridynamics

Xue Liang^1,2, Linjuan Wang^3,*

1 State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China
2 CAPT-HEDPS, and IFSA Collaborative Innovation Center of MoE, College of Engineering, Peking University, Beijing, 100871, China
3 School of Astronautics, Beihang University, Beijing, 100191, China

* Corresponding Author: Linjuan Wang. Email:

Computer Modeling in Engineering & Sciences 2024, 139(3), 2807-2834. https://doi.org/10.32604/cmes.2024.046770

Received 14 October 2023; Accepted 26 December 2023; Issue published 11 March 2024

Abstract

The peridynamics (PD), as a promising nonlocal continuum mechanics theory, shines in solving discontinuous problems. Up to now, various numerical methods, such as the peridynamic mesh-free particle method (PD-MPM), peridynamic finite element method (PD-FEM), and peridynamic boundary element method (PD-BEM), have been proposed. PD-BEM, in particular, outperforms other methods by eliminating spurious boundary softening, efficiently handling infinite problems, and ensuring high computational accuracy. However, the existing PD-BEM is constructed exclusively for bond-based peridynamics (BBPD) with fixed Poisson’s ratio, limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems. In this paper, we address these limitations by introducing the boundary element method (BEM) for ordinary state-based peridynamics (OSPD-BEM). Additionally, we present a crack propagation model embedded within the framework of OSPD-BEM to simulate crack propagations. To validate the effectiveness of OSPD-BEM, we conduct four numerical examples: deformation under uniaxial loading, crack initiation in a double-notched specimen, wedge-splitting test, and three-point bending test. The results demonstrate the accuracy and efficiency of OSPD-BEM, highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios. Moreover, OSPD-BEM significantly reduces computational time and exhibits greater consistency with experimental results compared to PD-MPM.

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Keywords

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